A particular example of a winner determination problem is the winner determination problem for auctions. For example, consider a reverse auction in which a number of sellers provide bids for supplying quantities of a variety of goods and/or services. It would be desirable to have an automatic system capable of providing the best set of bids to accept.
A difficulty may arise in that often there will be some form of constraint on the process so that the winner determination problem is not simply a question of selecting the set of bids which generate the lowest cost. For example, there may be a desire to have at least two suppliers, to avoid over-reliance on a single supplier, but not too many suppliers, to avoid excessive costs in procurement and delivery. It may be very hard to mathematically represent such constraints. For example, it may be very difficult to represent the desire not to have “too many suppliers” since it may not be clear at the start of the auction how many suppliers represents “too many”.